Are you trying to show the whole thing in one screen? If so you will probably want the dimensons to be 16 : 9 otherwise you might have to put black bars on the edges or have weird pixel distortion If you have a camera that moves around and say follows a character, then size / ratio of the camera and the size / ratio of the background scenery dont really interact to much unless you want to zoom out fully.

If your camera is just going to follow the hero then you want the aspect ratio of the camera to be based on computer resolution apect ratios. I'd go with something 16:9, but the actual size depends on how big you want the screen to feel. 1280:720 if you want to show alot of background, or maybe 640: 360 if you want it to feel really close to the player. The size of your character and the amount of background you want showing is kind of what determins this. 960:540 maybe